On-off keying-7-phase shift keying modulation system and method for fiber communication

ABSTRACT

A modulation system includes a modulator configured to employ a modulation mechanism on data. The mechanism includes a signal constellation configured to map sub-carriers which include a signal to be modulated. The signal constellation has a plurality of points asymmetrically disposed on a circle about an origin and a point at the origin wherein a number of sub-carriers becomes variable over different symbol intervals. Corresponding demodulators and corresponding methods are also disclosed.

RELATED APPLICATION INFORMATION

This application claims priority to provisional application Ser. No.60/913,859 filed on Apr. 25, 2007, incorporated herein by reference.

BACKGROUND

1. Technical Field

The present invention relates to signal modulation and more particularlyto a modulation system and method that improve power efficiency andreduces inter-carrier interference (ICI).

2. Description of the Related Art

Orthogonal Frequency Division Multiplexing (OFDM) has achieved greatsuccess in wireless and cable communications due to its robustnessagainst multipath fading and its potential for high spectral efficiency.However, OFDM is sensitive to frequency distortion. For optical fibercommunication, chromatic dispersion (CD) and polarization modedispersion (PMD) have similar frequency distortion effects. Tocompensate for these dispersions, and to take advantage of the highspectral efficiency, the OFDM applications in optical systems have begunto be investigated.

Directly applying OFDM into optical systems has at least the followingproblems: (a) sensitivity to carrier frequency offset (CFO) caused bythe misalignment in carrier frequencies between transmitter andreceiver; (b) sensitivity to the receiver In-phase and Quadrature (IQ)imbalance due to manufacturing inaccuracies. Both CFO and IQ imbalancewill cause Inter-Carrier Interference (ICI) among the sub-carriers anddecrease the Carrier-to-Interference Ratio (CIR), thus degrading systemperformance.

Referring to FIG. 1, a signal constellation for 8-PSK (8-phase shiftkeying) is illustratively shown. OFDM systems using conventional 8-PSK,whose signal constellation is shown in FIG. 1, use all sub-carrierssimultaneously to transmit modulated symbols. The number of sub-carriersand the separation between the sub-carriers are fixed all the time. Whenthe CFO and the IQ imbalances exist, all sub-carriers will contribute tothe ICI, which will degrade system performance. Due to the fact that allsub-carriers are used all the time, there is no power efficiencyimprovement.

An OFDM system using 8-PSK modulation uses modulated signal waveformsfor 8-PSK which can be expressed as

$\begin{matrix}{{{{s_{m}(t)} = {{{g(t)}{\cos\lbrack {{2\pi\; f_{c}t} + {\frac{2\pi}{8}( {m - 1} )}} \rbrack}\mspace{14mu} 1} \leq m \leq 8}},{0 \leq t \leq T}}{where}} & (1)\end{matrix}$g(t) is the pulse shape, t is time, T is the period or symbol duration,f_(c) is the carrier frequency.

SUMMARY

A modulation system includes a modulator configured to employ amodulation mechanism on data. The mechanism includes a signalconstellation configured to map sub-carriers which include a signal tobe modulated. The signal constellation has a plurality of pointsasymmetrically disposed on a circle about an origin and a point at theorigin wherein a number of sub-carriers become variable over differentsymbol intervals. Corresponding demodulators and corresponding methodsare also disclosed.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a constellation diagram showing 8 phase shift keying inaccordance with the prior art;

FIG. 2 is a block/flow diagram showing a transceiver with correspondingtransmitter and receiver portions employing on-off keying-7 phase shiftkeying (OOK-7-PSK) in accordance with one illustrative embodiment;

FIG. 3 is a constellation diagram showing OOK-7-PSK in accordance withthe present principles;

FIG. 4 is a block diagram demonstrating phase and amplitude imbalancesto be accounted for at a receiver;

FIG. 5 is a plot of CIR versus normalized frequency offset for differentIQ imbalances;

FIG. 6 is a plot symbol error rate (SER) versus signal to noise ratio(SNR) under the conditions of ε=0.01, δ=0.1, and φ=10°; and

FIG. 7 is a plot symbol error rate (SER) versus signal to noise ratio(SNR) changing the conditions to ε=0.05, δ=0.2, and φ=10°.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present embodiments present an orthogonal frequency divisionmultiplexing (OFDM) optical system using On-Off-Keying7-Phase-Shift-Keying (OOK-7PSK) modulation that provides improved powerefficiency and reduced inter-carrier interference (ICI). The OFDM systemusing On-Off-Keying 7-Phase-Shift-Keying (OOK-7PSK) modulation, whichincludes seven evenly spaced points on a circle plus a point at theorigin, reduces the ICI in high-data-rate fiber communication systems.The numerical and simulation results show that the OFDM system usingOOK-7PSK is more robust against both CFO and IQ imbalance compared tothe OFDM system using conventional 8-PSK modulation. The OOK-7PSKmodulation reduces Inter-Carrier interference and improves the powerefficiency. These benefits are achieved without additional systemcomplexity.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in hardware withpossible software elements. Software includes but is not limited tofirmware, resident software, microcode, etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable medium such as a semiconductor or solid state memory,magnetic tape, a removable computer diskette, a random access memory(RAM), a read-only memory (ROM), a rigid magnetic disk and an opticaldisk, etc.

The present embodiments may be provided and used in anytransmitter/receiver application. The present system and method may beemployed in electrical signaling systems, optical signaling systems orany other signaling system or network.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIG. 2, a block/flow diagram of anOFDM system 100 is depicted in accordance with the present principles.System 100 shows both a transmitter 150 and a receiver 160. Thesecomponents may be employed together or separately as needed. An OOK-7PSKmodulator 102 is employed in this system, whose constellation is shownin FIG. 3. The effects of CFO and IQ imbalance have been considered andwill be discussed hereinafter.

An input data stream 101 from a data source is first modulated byOOK-7PSK modulator 102, resulting in a serial complex symbol stream.This symbol stream 101 is passed through a serial-to-parallel converter(S/P) 104, whose output is a set of N parallel symbols. Then, these Nparallel symbols in frequency domain are converted into samples in timedomain by taking an inverse Fast Fourier Transform (IFFT) 106. The IFFT106 yields the OFDM symbols including the sequence of length N, whichcorresponds to samples of the multi-carrier signal that includeslinearly modulated sub-carriers. Then, in block 108, a cyclic prefix(CP) is added to the OFDM symbol to avoid Inter-Symbol Interference(ISI), and the resulting time symbols are converted from parallel toserial (P/S) (block 108). The time symbols are passed through a digitalto analog (D/A) converter and a low-pass filter (LPF) 110.

A final resulting OFDM signal is then upconverted using mixer 112 to acarrier frequency f_(c) 114 and provided on a channel 116.

A receiver portion 160 performs the opposite functions of thetransmitter 150. An OFDM signal is downconverted using mixer 118 to thecarrier frequency f_(c) 120 from channel 116. The transmitted signalfrom channel 116 may be filtered by a channel impulse response andcorrupted by Additive White Gaussian Noise (AWGN) in simulations. Thetransmitted OFDM signal is impaired by the CFO (Δf ′) and IQ imbalance.The time symbols are passed through a low-pass filter (LPF) and ananalog to digital (A/D) converter 122. In block 124, the cyclic prefix(CP) is deleted from the OFDM symbol, and the resulting time symbols areconverted from serial to parallel (S/P) (block 124). Then, these Nparallel symbols in time domain are converted into samples in frequencydomain by taking a Fast Fourier Transform (FFT) 126. The symbol streamis passed through a parallel-to-serial converter (P/S) 128, which takesa set of N parallel symbols and serially inputs them to a demodulator130. Demodulators 130 demodulates by OOK-7PSK, resulting in a serialcomplex symbol stream output to a data sink 131.

Referring to FIG. 3, OOK-7PSK in accordance with the present inventionincludes a 7-PSK constellation 202 plus a point 204 at the origin. Whendata information is mapped to the point 204 at the origin, thecorresponding sub-carrier is not used for transmission, i.e., there isno power to be transmitted on that sub-carrier, which will notcontribute to ICI. Hence, the resulting number of sub-carriers for thepresent system using OOK-7PSK becomes variable, which means differentnumbers of sub-carriers are transmitted over different symbol intervals,resulting in a variable sub-carrier OFDM system. Since not allsub-carriers are transmitted simultaneously all the time, powerefficiency can be increased and the average ICI in the OFDM system canbe decreased, which results in performance improvements.

The OFDM system using OOK-7PSK modulation, whose signal constellationincludes seven evenly spaced points 208 on a circle 206 plus the point204 at the origin, provides signal waveforms that can be expressed as:

$\begin{matrix}{{s_{m}(t)} = \{ {{\begin{matrix}{{g(t)}{\cos\lbrack {{2\pi\; f_{c}t} + {\frac{2\pi}{7}( {m - 1} )}} \rbrack}} & ( {1 \leq m \leq 7} ) \\0 & ( {m = 8} )\end{matrix}0} \leq t \leq T} } & (2)\end{matrix}$where g(t) is the pulse shape of the transmitted signal and T is theduration of the symbol.

When data is mapped to the point at the origin, the correspondingsub-carrier is not used for transmission, i.e., there is no power to betransmitted on that sub-carrier, which will not contribute to the ICIwhen the CFO and the IQ imbalance exist. Hence, the resulting numbers ofsub-carriers using OOK-7PSK modulation becomes variable, so that theaverage separation between sub-carriers is increased, resulting in theprobability of symbol error being improved. The points 208 areasymmetrically disposed about the axes passing through the origin.

Not all sub-carriers being transmitted at the same time has ⅛probability of not being transmitted. Hence, the average CIR for thepresent OFDM system using OOK-7PSK modulation can be expressed as

$\begin{matrix}\begin{matrix}{{CIR}_{{OOK} - {7{PSK}}} = \frac{{{{X(k)}{S(0)}}}^{2}}{E\lbrack {{\sum\limits_{{l = 0},{l \neq k}}^{N - 1}{{X(l)}{S( {l - k} )}}}}^{2} \rbrack}} \\{= \frac{{{S(0)}}^{2}}{( {7/8} ){\sum\limits_{l = 1}^{N - 1}{{S(l)}}^{2}}}} \\{= {( {8/7} ){CIR}_{8\text{-}{PSK}}}}\end{matrix} & (3)\end{matrix}$

IQ Imbalance: The effect caused by IQ imbalance is now considered.Referring to FIG. 4, IQ imbalance at the receiver is illustrativelyshown. In a conventional OFDM system, IQ imbalance can be characterizedby two parameters: the amplitude imbalance between I and Q channel, andthe phase imbalance. The complex baseband signal x(t) is up-converted tothe desired carrier frequency (f_(c)), and then amplified beforetransmission. At the receiver, a down-converted and low-pass filtered(LPF) RF signal is sampled to yield the sequence for FFT demodulation.The IQ imbalance at the receiver distorts this received signal. Thereceived signal on the k^(th) sub-carrier after the FFT can be expressedas:Y(k)=αX(k)+βX*(N−1−k)+N(k)  (4)wherek=0,1, . . . N−1α=0.5{1+(1+δ)(cos φ−j sin φ)}where δ is the amplitude imbalanceβ=0.5{1−(1+δ)(cos φ+j sin φ)}and φ is the phase imbalance at the receiver.

Equation (4) shows that the gain and phase mismatches in the receivercause the symbol at the sub-carrier k to be multiplied by the complexfactor α. In addition, a spurious component will be present which isequal to the conjugate of the symbol at the (N−1−k)^(th) sub-carriermultiplied by another complex factor β. The symbol at the k^(th)sub-carrier will include an interference related to the symbol at the(N−1−k)^(th) sub-carrier, and vice versa.

As mentioned, in OFDM systems using conventional 8-PSK modulation, allsub-carriers are used to transmit information, hence, the IQ imbalancewill result in each sub-carrier being interfered with by its frequencymirror-image sub-carrier. All of them will contribute to ICI. However,in the OFDM system using OOK-7PSK modulation, the sub-carriers may notbe transmitted at the same time, thus the average ICI caused by usingOOK-7PSK modulation is just ⅞ of the ICI caused by using 8-PSKmodulation when IQ imbalance exists.

Joint Impairment: We have considered the effects of CFO and IQ-imbalanceseparately. Normally, the received signal may be affected by their jointimpairments. We need to consider the joint effects of CFO and IQimbalance. The received signal on the k^(th) sub-carrier after the FFTprocessing can be expressed as

$\begin{matrix}{{\hat{Y}(k)} = {{\alpha\;{X(k)}{S(0)}} + {\sum\limits_{{l = 0},{l \neq k}}^{N - 1}{\alpha\;{X(l)}{S( {l - k} )}}} + {\sum\limits_{i = 0}^{N - 1}{\beta\;{X^{*}(l)}{S^{*}( {l - ( {N - 1 - k} )} )}}} + {\alpha\;{N(k)}} + {\beta\;{N^{*}( {N - 1 - k} )}\text{)}}}} & (5)\end{matrix}$

while this joint IQ imbalance and CFO causes more ICI, the average CIRfor an OFDM system can be expressed as The average CIR for the proposedOFDM system using OOK-7PSK can be expressed as

$\begin{matrix}\begin{matrix}{{CIR}_{{OOK}\text{-}7{PSK}} = \frac{{{\alpha\;{S(0)}}}^{2}}{( {7/8} )\{ {{{\alpha }^{2}{\sum\limits_{l = 1}^{N - 1}{{S(l)}}^{2}}} + {{\beta }^{2}{\sum\limits_{l = 0}^{N - 1}{{S^{*}( {l - N + 1} )}}^{2}}}} \}}} \\{= {( {8/7} ){CIR}_{8 - {PSK}}}}\end{matrix} & (6)\end{matrix}$

Referring to FIG. 5, average CIRs between an OFDM system using 8-PSK andthe OFDM system using OOK-7PSK for a normalized frequency offset εvarying from 0.01 to 0.25 with different IQ imbalances is shown. Thenumber of sub-carriers is 256. FIG. 5 shows CIRs versus normalizedfrequency offset with different IQ imbalances. Note that, as the CFOincreases, the CIR decreases. The CIRs of OOK-7PSK perform at least 0.58dB better than the ones of 8-PSK. Also, when the IQ imbalance increases,the CIRs for both OFDM systems decrease over all CFOs.

Referring to FIGS. 6-7 and tables 1-2, symbol error rate (SER)performances for an OFDM system using conventional 8-PSK and the OFDMsystem using OOK-7PSK with different IQ imbalances at different CFOs areshown. As CFO and IQ imbalance changes, the signal to noise (SNR) gainsbetween the present OFDM system and a conventional OFDM system are alsochanged. In FIG. 6, the SNR gain is 1.8 dB in favor of the OOK-7PSK at aSER of 10⁻³ under the conditions of ε=0.01, δ=0.1, and φ=10°. FIG. 7shows SER versus SNR for the following conditions: ε=0.05, δ=0.2, andφ=10°.

Table 1 shows the gains between the OOK-7PSK and conventional 8-PSK withthe fixed IQ imbalance of δ=0.05, φ=5° at different CFOs. When the CFOis increased from 0.01 to 0.10, the gain between the OOK-7PSK andconventional 8-PSK is increased from 1.85 dB to 4.62 dB.

TABLE 1 δ = 0.05, φ = 5° OOK-7PSK 8-PSK GAIN ε SER (E_(b)/N₀)(dB)(E_(b)/N₀)(dB) (dB) 0.01 10⁻³ 10.00 11.15 1.15 0.05 10⁻³ 11.15 12.951.80 0.10 10⁻² 11.53 16.15 4.62

Table 2 shows the gains between the OOK-7PSK and conventional 8-PSK withthe fixed CFO of ε=0.10 at different IQ imbalances. We note that, whenthe IQ imbalance is changed from δ=0.05, φ=5° to δ=0.20, φ=10°, the gainbetween the OOK-7PSK and conventional 8-PSK is changed from 1.85 dB to6.70 dB at a SER of 10⁻³.

TABLE 2 ε = 0.10 OOK-7PSK 8-PSK GAIN δ/φ SER (E_(b)/N₀)(dB)(E_(b)/N₀)(dB) (dB) 0.05/5  10⁻³ 11.10 12.95 1.85 0.10/10 10⁻³ 12.2515.45 3.20 0.20/10 10⁻³ 13.30 20.00 6.70

A comparison between FIGS. 6-7 and Tables 1-2 shows that the OFDM systemusing OOK-7PSK modulation is rather robust to CFO and IQ imbalancescompared with an OFDM system using conventional 8-PSK modulation.Therefore, the present OFDM system can be used in the case where CFO andIQ imbalance exist.

An OFDM system using OOK-7PSK modulation has been disclosed and the SERperformances under the effects of both CFO and IQ imbalance have beenanalyzed. By using OOK-7PSK modulation, the present OFDM system obtainsSNR gains and improves power efficiency by at least 12.5%. Allsimulation results have shown that the present OFDM system usingOOK-7PSK modulation performs better than an OFDM system usingconventional 8-PSK modulation especially under the effects of both CFOand IQ imbalance.

Having described preferred embodiments for an on-off keying-7-phaseshift keying modulation system and method for fiber communication (whichare intended to be illustrative and not limiting), it is noted thatmodifications and variations can be made by persons skilled in the artin light of the above teachings. It is therefore to be understood thatchanges may be made in the particular embodiments disclosed which arewithin the scope and spirit of the invention as outlined by the appendedclaims. Having thus described aspects of the invention, with the detailsand particularity required by the patent laws, what is claimed anddesired protected by Letters Patent is set forth in the appended claims.

1. A modulation system, comprising: a modulator configured to employ amodulation mechanism on data, the mechanism including: a signalconstellation configured to map sub-carriers which comprise a signal tobe modulated, the signal constellation including a plurality of pointsasymmetrically disposed on a circle about an origin and a point at theorigin wherein a number of sub-carriers becomes variable over differentsymbol intervals.
 2. The system as recited in claim 1, wherein theconstellation includes 7 evenly spaced points on the circle.
 3. Thesystem as recited in claim 1, wherein the 7 evenly spaced points on thecircle are asymmetrical relative to axes defined by the origin.
 4. Thesystem as recited in claim 1, wherein the mechanism includes on-offkeying-7 phase shift keying (OOK-7PSK).
 5. The system as recited inclaim 1, wherein when data is mapped to the origin, no correspondingsub-carrier is used for transmission.
 6. The system as recited in claim5, wherein when data is mapped to the origin, no power is transmittedand no contribution to Inter-Carrier Interference (ICI).
 7. The systemas recited in claim 5, wherein power efficiency is increased by at least12.5% over 8-PSK.
 8. The system as recited in claim 1, wherein whenmapping to the origin, no corresponding sub-carrier is used fortransmission.
 9. A modulation system, comprising: a demodulatorconfigured to employ a demodulation mechanism on data which accounts forat least IQ imbalance and carrier frequency offset (CFO) in a receivedsignal, the mechanism including: a signal constellation configured tomap sub-carriers which comprise a signal to be demodulated, the signalconstellation including a plurality of points asymmetrically disposed ona circle about an origin and a point at the origin wherein a number ofsub-carriers becomes variable over different symbol intervals.
 10. Thesystem as recited in claim 9, wherein the constellation includes 7evenly spaced points on the circle.
 11. The system as recited in claim9, wherein the 7 evenly spaced points on the circle are asymmetricalrelative to axes defined by the origin.
 12. The system as recited inclaim 9, wherein the mechanism includes on-off keying-7 phase shiftkeying (OOK-7PSK).
 13. The system as recited in claim 9, wherein when nocorresponding sub-carrier is present data is mapped to the origin. 14.The system as recited in claim 9, wherein when no power is transmitted,data is mapped to the origin.
 15. A modulation method, comprising:modulating a signal using an on-off keying-7 phase shift keying(OOK-7-PSK) modulation mechanism which includes a signal constellation;and mapping sub-carriers which comprise a signal to be modulated to thesignal constellation, which includes a plurality of pointsasymmetrically disposed on a circle about an origin and a point at theorigin wherein a number of sub-carriers becomes variable over differentsymbol intervals.
 16. The method as recited in claim 15, wherein theconstellation includes 7 evenly spaced points on the circle.
 17. Themethod as recited in claim 15, wherein the 7 evenly spaced points on thecircle are asymmetrical relative to axes defined by the origin.
 18. Amodulation method, comprising: demodulating a signal using an on-offkeying-7 phase shift keying (OOK-7-PSK) demodulation mechanism whichaccounts for at least IQ imbalance and carrier frequency offset (CFO) ina received signal, and includes a signal constellation; and mappingsub-carriers which comprise a signal to be demodulated to the signalconstellation which includes a plurality of points asymmetricallydisposed on a circle about an origin and a point at the origin wherein anumber of sub-carriers becomes variable over different symbol intervals.19. The method as recited in claim 18, wherein the constellationincludes 7 evenly spaced points on the circle.
 20. The method as recitedin claim 18, wherein the 7 evenly spaced points on the circle areasymmetrical relative to axes defined by the origin.
 21. The method asrecited in claim 18, wherein when no corresponding sub-carrier ispresent data is mapped to the origin.